The structure of classical extensions of quantum probability theory

On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra–Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed

Unsharp Quantum Reality

The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency-or potentiality-of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way

Decomposition and primary crystallization in undercooled Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 melts

Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 bulk metallic glasses were prepared by cooling the melt with a rate of about 10 K/s and investigated with respect to their chemical and structural homogeneity by atom probe field ion microscopy and transmission electron microscopy. The measurements on these slowly cooled samples reveal that the alloy exhibits phase separation in the undercooled liquid state. Significant composition fluctuations are found in the Be and Zr concentration but not in the Ti, Cu, and Ni concentration. The decomposed microstructure is compared with the microstructure obtained upon primary crystallization, suggesting that the nucleation during primary crystallization of this bulk glass former is triggered by the preceding diffusion controlled decomposition in the undercooled liquid state

Vortex Dynamics in Anisotropic Traps

We investigate the dynamics of linear vortex lattices in anisotropic traps in two-dimensions and show that the interplay between the rotation and the anisotropy leads to a rich but highly regular dynamics.Comment: 6 pages, 6 figure

Approximating incompatible von Neumann measurements simultaneously

We study the problem of performing orthogonal qubit measurements simultaneously. Since these measurements are incompatible, one has to accept additional imprecision. An optimal joint measurement is the one with the least possible imprecision. All earlier considerations of this problem have concerned only joint measurability of observables, while in this work we also take into account conditional state transformations (i.e., instruments). We characterize the optimal joint instrument for two orthogonal von Neumann instruments as being the Luders instrument of the optimal joint observable.Comment: 9 pages, 4 figures; v2 has a more extensive introduction + other minor correction

Quantum Mechanics as a Framework for Dealing with Uncertainty

Quantum uncertainty is described here in two guises: indeterminacy with its concomitant indeterminism of measurement outcomes, and fuzziness, or unsharpness. Both features were long seen as obstructions of experimental possibilities that were available in the realm of classical physics. The birth of quantum information science was due to the realization that such obstructions can be turned into powerful resources. Here we review how the utilization of quantum fuzziness makes room for a notion of approximate joint measurement of noncommuting observables. We also show how from a classical perspective quantum uncertainty is due to a limitation of measurability reflected in a fuzzy event structure -- all quantum events are fundamentally unsharp.Comment: Plenary Lecture, Central European Workshop on Quantum Optics, Turku 2009

Approximate joint measurement of qubit observables through an Arthur-Kelly type model

We consider joint measurement of two and three unsharp qubit observables through an Arthur-Kelly type joint measurement model for qubits. We investigate the effect of initial state of the detectors on the unsharpness of the measurement as well as the post-measurement state of the system. Particular emphasis is given on a physical understanding of the POVM to PVM transition in the model and entanglement between system and detectors.Two approaches for characterizing the unsharpness of the measurement and the resulting measurement uncertainty relations are considered.The corresponding measures of unsharpness are connected for the case where both the measurements are equally unsharp. The connection between the POVM elements and symmetries of the underlying Hamiltonian of the measurement interaction is made explicit and used to perform joint measurement in arbitrary directions. Finally in the case of three observables we derive a necessary condition for the approximate joint measurement and use it show the relative freedom available when the observables are non-orthogonal.Comment: 22 pages; Late